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1) ![left { {{x^{2} + y^{2} = 37} atop {xy=6}} right. ;<br />left { {{x^{2} + y^{2} = 37} atop {x= frac{6}{y}}} right. ;<br />left { {{ (frac{6}{y}) ^{2} + y^{2} =37 } atop {x=frac{6}{y}}} right.
left { {{x^{2} + y^{2} = 37} atop {xy=6}} right. ;<br />left { {{x^{2} + y^{2} = 37} atop {x= frac{6}{y}}} right. ;<br />left { {{ (frac{6}{y}) ^{2} + y^{2} =37 } atop {x=frac{6}{y}}} right.](https://tex.z-dn.net/?f=%0A+left+%7B+%7B%7Bx%5E%7B2%7D+%2B+y%5E%7B2%7D+%3D+37%7D+atop+%7Bxy%3D6%7D%7D+right.+%3B%26lt%3Bbr+%2F%26gt%3Bleft+%7B+%7B%7Bx%5E%7B2%7D+%2B+y%5E%7B2%7D+%3D+37%7D+atop+%7Bx%3D+frac%7B6%7D%7By%7D%7D%7D+right.+%3B%26lt%3Bbr+%2F%26gt%3Bleft+%7B+%7B%7B++%28frac%7B6%7D%7By%7D%29+%5E%7B2%7D+%2B++y%5E%7B2%7D+%3D37+%7D+atop+%7Bx%3Dfrac%7B6%7D%7By%7D%7D%7D+right.+)
![(frac{6}{y}) ^{2} + y^{2} =37 (frac{6}{y}) ^{2} + y^{2} =37](https://tex.z-dn.net/?f=%28frac%7B6%7D%7By%7D%29+%5E%7B2%7D+%2B+y%5E%7B2%7D+%3D37)
![frac{36}{ y^{2} } + y^{2} =37 frac{36}{ y^{2} } + y^{2} =37](https://tex.z-dn.net/?f=+frac%7B36%7D%7B+y%5E%7B2%7D+%7D+%2B++y%5E%7B2%7D++%3D37)
ОДЗ:
; ![y neq 0 y neq 0](https://tex.z-dn.net/?f=y+neq+0)
![36 + y^{4} = 37y^{2} 36 + y^{4} = 37y^{2}](https://tex.z-dn.net/?f=36+%2B++y%5E%7B4%7D+%3D+37y%5E%7B2%7D+)
![y^{4} - 37y^{2} +36 =0 y^{4} - 37y^{2} +36 =0](https://tex.z-dn.net/?f=+y%5E%7B4%7D+-+37y%5E%7B2%7D+%2B36+%3D0)
Пусть![y^{2} = t, t geq 0 y^{2} = t, t geq 0](https://tex.z-dn.net/?f=+y%5E%7B2%7D+%3D+t%2C+t+geq+0)
![t^{2} - 37t+36=0 t^{2} - 37t+36=0](https://tex.z-dn.net/?f=+t%5E%7B2%7D+-+37t%2B36%3D0)
×
×
корня
![t_{1} = frac{37+35}{2} = 36 t_{1} = frac{37+35}{2} = 36](https://tex.z-dn.net/?f=t_%7B1%7D+%3D+frac%7B37%2B35%7D%7B2%7D+%3D+36)
![t_{2} = frac{37-35}{2} = 1 t_{2} = frac{37-35}{2} = 1](https://tex.z-dn.net/?f=t_%7B2%7D+%3D+frac%7B37-35%7D%7B2%7D+%3D+1)
![y^{2} =36
<br /><br />y_{1} = -6; y_{2} = 6 y^{2} =36
<br /><br />y_{1} = -6; y_{2} = 6](https://tex.z-dn.net/?f=+y%5E%7B2%7D+%3D36%0A%26lt%3Bbr+%2F%26gt%3B%26lt%3Bbr+%2F%26gt%3By_%7B1%7D+%3D+-6%3B++y_%7B2%7D+%3D+6)
![y^{2} =1<br /><br />y_{3} = -1; y_{4} =1 y^{2} =1<br /><br />y_{3} = -1; y_{4} =1](https://tex.z-dn.net/?f=+y%5E%7B2%7D+%3D1%26lt%3Bbr+%2F%26gt%3B%26lt%3Bbr+%2F%26gt%3By_%7B3%7D+%3D+-1%3B++y_%7B4%7D+%3D1)
![x_{1} = frac{6}{-6} = -1 x_{1} = frac{6}{-6} = -1](https://tex.z-dn.net/?f=+x_%7B1%7D+%3D+frac%7B6%7D%7B-6%7D+%3D+-1)
![x_{2} = frac{6}{6} =1 x_{2} = frac{6}{6} =1](https://tex.z-dn.net/?f=+x_%7B2%7D+%3D++frac%7B6%7D%7B6%7D+%3D1)
![x_{3} = frac{6}{-1} = -6 x_{3} = frac{6}{-1} = -6](https://tex.z-dn.net/?f=+x_%7B3%7D+%3D++frac%7B6%7D%7B-1%7D+%3D+-6)
![x_{4} = frac{6}{1} = 6 x_{4} = frac{6}{1} = 6](https://tex.z-dn.net/?f=+x_%7B4%7D+%3D++frac%7B6%7D%7B1%7D+%3D+6)
Ответ:
ОДЗ:
Пусть
Ответ:
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